Question

How many of the $900$ three digit numbers have at least one even digit?

• A. $775$
• B. $875$
• C. $450$
• D. $750$

Answer 1

Answer: (A)

$775$

For a $3$ digit number using $0,1,2,...9$

Option for hundred'th placed digit$=9$ ($0$ excluded)

Option for ten'th placed digit$=10$

Option for unit placed digit$=10$

Total $3$ digit numbers $=9\times 10\times 10=900$

Now, Option for hundred'th placed odd digit$=1,3,5,7,9=5$(only odd digits)

Option for ten'th odd digit$=5$

option for unit placed odd digit$=5$

Total $3$ digit numbers with all odd digits$=5\times 5\times 5=125$

Total $3$ digit numbers with atleast one even digit$=900-125=775$